Self‐consistent hybridization expansions for static properties of the Anderson impurity model

Hamad, I. J.; Roura‐Bas, P.; Aligia, A. A.; Anda, E. V.

doi:10.1002/pssb.201552414

Cited by 4 publications

(9 citation statements)

References 46 publications

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“…For N =2 we include in the figure results obtained using the Bethe ansatz (BA) as described in Ref. 81. These results were shifted to the left by a constant energy C to compensate by the Haldane shift and possible uncertainties in the position of E d in the BA treatment.…”

Section: Occupancy For Su(2) and Su(4)mentioning

confidence: 99%

Width of the charge-transfer peak in the SU( N ) impurity Anderson model and its relevance to nonequilibrium transport

et al. 2018

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We calculate the width 2∆CT and intensity of the charge-transfer peak (the one lying at the onsite energy E d ) in the impurity spectral density of states as a function of E d in the SU(N ) impurity Anderson model (IAM). We use the dynamical density-matrix renormalization group (DDMRG) and the noncrossing-approximation (NCA) for N =4, and a 1/N variational approximation in the general case. In particular, while for E d ≫ ∆, where ∆ is the resonant level half-width, ∆CT = ∆ as expected in the noninteracting case, for −E d ≫ N ∆ one has ∆CT = N ∆. In the N =2 case, some effects of the variation of ∆CT with E d were observed in the conductance through a quantum dot connected asymmetrically to conducting leads at finite bias [J. Könemann et al., Phys. Rev. B 73, 033313 (2006)]. More dramatic effects are expected in similar experiments, that can be carried out in systems of two quantum dots, carbon nanotubes or other, realizing the SU(4) IAM.

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Section: Occupancy For Su(2) and Su(4)mentioning

confidence: 99%

Width of the charge-transfer peak in the SU( N ) impurity Anderson model and its relevance to nonequilibrium transport

et al. 2018

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“…( 1). We proceed by projecting its Hilbert space into two subspaces, S 1 and S 2 , and constructing a renormalized Hamiltonian H ren that operates in just one of them 36,37 . For the case of subspace S 1 , H ren can be written as 65 ,…”

Section: B Projection Operator Approachmentioning

confidence: 99%

“…Among the most largely utilized we can mention the Numerical Renormalization Group (NRG) 32 , the Density Matrix Renormalization Group (DMRG) 33 , and the Logarithmic Discretized Embedded Cluster Approximation (LDECA) 34 . Other algebraic approaches have as well been used as the various Slave Boson Approximations 35 and Projection Operator Approach (POA) 36,37 and others based on the Green's function formalism as the Non-Crossing and One-Crossing Approximation (NCA, OCA) [38][39][40] , and the equation of motion method 41 . In addition, it should be mentioned the use of the Perturbative Renormalized Group Approach 42,43 as well as extensions of Noziere's Fermi liquid-like theories [44][45][46] .…”

Section: Introductionmentioning

confidence: 99%

“…It will be shown in Section V that a relatively small magnetic field can polarize the current transmitted through the QDs with a polarization parallel to the field for embedded QDs and antiparallel to it in the case of side-coupled QDs, as schematically illustrated in panels (a) and (b), respectively. This phenomenology is studied adopting two different formalisms: (i) the Mean Field Slave Bosons Approximation (MFSBA) [57][58][59][60][61][62] , which allows an approximate analysis of the dynamical properties of the system, and (ii) the POA, which has been shown to describe, almost exactly, the static properties associated to the ground state of the Anderson Impurity Hamiltonian 36,37 . Note that we have extended the POA, originally derived to study single-impurity Kondo problems, to the analysis of two capacitively-coupled local levels.…”

Section: Introductionmentioning

confidence: 99%

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SU(4)-SU(2) crossover and spin-filter properties of a double quantum dot nanosystem

et al. 2017

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The SU (4)−SU (2) crossover, driven by an external magnetic field h, is analyzed in a capacitivelycoupled double-quantum-dot device connected to independent leads. As one continuously charges the dots from empty to quarter-filled, by varying the gate potential Vg, the crossover starts when the magnitude of the spin polarization of the double quantum dot, as measured by n ↑ − n ↓ , becomes finite. Although the external magnetic field breaks the SU (4) symmetry of the Hamiltonian, the ground state preserves it in a region of Vg, where n ↑ − n ↓ = 0. Once the spin polarization becomes finite, it initially increases slowly until a sudden change occurs, in which n ↓ (polarization direction opposite to the magnetic field) reaches a maximum and then decreases to negligible values abruptly, at which point an orbital SU (2) ground state is fully established. This crossover from one Kondo state, with emergent SU (4) symmetry, where spin and orbital degrees of freedom all play a role, to another, with SU (2) symmetry, where only orbital degrees of freedom participate, is triggered by a competition between gµBh, the energy gain by the Zeeman-split polarized state and the Kondo temperature T SU (4) K , the gain provided by the SU (4) unpolarized Kondo-singlet state. At fixed magnetic field, the knob that controls the crossover is the gate potential, which changes the quantum dots occupancies. If one characterizes the occurrence of the crossover by V max g , the value of Vg where n ↓ reaches a maximum, one finds that the function f relating the Zeeman splitting, Bmax, that corresponds to V max g , i.e., Bmax = f V max g , has a similar universal behavior to that of the function relating the Kondo temperature to Vg. In addition, our numerical results show that near the SU (4) Kondo temperature and for relatively small magnetic fields the device has a ground state that restricts the electronic population at the dots to be spin polarized along the magnetic field. These two facts introduce very efficient spin-filter properties to the device, also discussed in detail in the paper. This phenomenology is studied adopting two different formalisms: the Mean Field Slave Bosons Approximation, which allows an approximate analysis of the dynamical properties of the system, and a Projection Operator Approach, which has been shown to describe very accurately the physics associated to the ground state of Kondo systems.

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“…Some tricks to evaluate integrals that enter these expressions are given in the appendix of Ref. [52].…”

Section: Summary and Discussionmentioning

confidence: 99%

Leading temperature dependence of the conductance in Kondo-correlated quantum dots

Aligia¹

2018

J. Phys.: Condens. Matter

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Using renormalized perturbation theory in the Coulomb repulsion, we derive an analytical expression for the leading term in the temperature dependence of the conductance through a quantum dot described by the impurity Anderson model, in terms of the renormalized parameters of the model. Taking these parameters from the literature, we compare the results with published ones calculated using the numerical renormalization group obtaining a very good agreement. The approach is superior to alternative perturbative treatments. We compare in particular to the results of a simple interpolative perturbation approach.

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Self‐consistent hybridization expansions for static properties of the Anderson impurity model

Cited by 4 publications

References 46 publications

Width of the charge-transfer peak in the SU( N ) impurity Anderson model and its relevance to nonequilibrium transport

Width of the charge-transfer peak in the SU( N ) impurity Anderson model and its relevance to nonequilibrium transport

SU(4)-SU(2) crossover and spin-filter properties of a double quantum dot nanosystem

Leading temperature dependence of the conductance in Kondo-correlated quantum dots

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